Such a construction forms part of a mechanical linear guide which is known from the lecture synopsis of M. P. Xoster, "Constructieprincipes voor het nauwkeurig bewegen en positioneren" ("Construction principles for accurately moving and positioning"), WA-163, University of Twente, October 1990, p. 172. In order to make only an axial movement possible in the known construction, the above-mentioned four suspension means and five points cannot lie in a flat plane. In the known construction the first three points lie in a first plane, and the third, fourth and fifth points lie in a second plane, which planes form an angle of 120.degree. with each other. Further suspension means are also provided, in such a way that a three-dimensional, symmetrical construction is produced and movement possibilities other than in the axial direction are eliminated. The known construction makes it possible for the body to move substantially only in an axial direction and for the lateral movement possibilities to be very small. However, for certain applications, the lateral deflections occurring herewith are still too great.